2000 AMC 8 Problem 11 — Solution | LIVE by Po-Shen Loh

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2000 AMC 8 Problem 11

Below is the professionally curated solution for Problem 11 of the 2000 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2000 AMC 8 solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:divisibility digits casework

Difficulty rating: 1140

11.

The number $64$ has the property that it is divisible by its unit digit. How many whole numbers between $10$ and $50$ have this property?

$15$

$16$

$17$

$18$

$20$

Solution:

Numbers ending in $1$ , $2$ , or $5$ all work in the ranges $11,21,31,41$ , $12,22,32,42$ , and $15,25,35,45$ . This gives $12$ numbers.

The remaining working numbers are $24,33,36,44,48$ . Numbers ending in $0$ do not work because division by $0$ is undefined.

Thus there are $12+5=17$ such numbers.

Thus, C is the correct answer.

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